1. What is the proper time period to beginning mailing materials to judges for judicial internships?

Some judges will interview you now. Others will wait until January/February/March.

If you want to work in the area of your school, I would send letters to judges in that area within the next few weeks. (EDIT: but the best thing to do is talk to 2Ls/3Ls who have interned for those judges and find out when the best time is to apply) If you want to interview "back home" or elsewhere over the winter break, I'd send those letters out around Thanksgiving. Even a lot of judges who don't typically hire until the spring will meet with you in December if you mention in your cover letter that you will be in that area over the break (and if your school is located far away).

2. I know that NALP firms don't want contact until Dec. 1. What about non-NALP firms? Should I still wait until December? Or earlier? Or wait until my 1st semester grades come out?

You can apply to non-NALP firms whenever you want. There's a high likelihood you will only get a firm job if you have stellar grades, so you might as well wait.

But if you are just looking to work for a small firm because you'd like to have some income during the summer, you might consider applying earlier.

If the money from a small firm is not a major concern, you might consider splitting the summer. You could apply to judges early and then see how grades turn out. Some judges will allow you to split the summer. This way, you line up a good internship early but still reserve the possibility of getting a well-paying firm job.